An interferometer is a well-known instrument for measuring properties of light or other waves. In its simplest form, an interferometer comprises a source of at least partially coherent waves, a splitter/combiner for splitting the waves into two portions and subsequently recombining them, two “arms” that the two split portions of waves propagate along and back prior to recombination, and a detector for detecting variations in the intensity of the recombined waves. Many variations exist, however; for example the splitting and combining may be carried out by separate elements, the arms may include waveguides or simply involve free-space propagation to a reflector of some kind, and there may in some cases be more than two arms. The significant property of an interferometer is that the intensity of the detected light waves with changes in the relative lengths of the arms, due to interference between the portions of waves that have propagated along each arm.
As is well-known, waves will interfere constructively (the instantaneous amplitudes will reinforce each other) when two or more identical waves are superimposed on each other in phase (such that peaks and troughs in each wave line up with each other), and will interfere destructively (the instantaneous amplitudes will cancel each other out) when such waves are superimposed on each other in anti-phase (such that peaks and troughs in one wave line up with troughs and peaks, respectively, in another wave). Phase differences that fall between fully in-phase and fully anti-phase interference result in reduced amounts of constructive or destructive interference, relative to those extreme cases. In an interferometer, as the length of an arm is increased, the wave that has traversed that arm will move in and out of phase with respect to an identical wave that has traversed an arm of fixed length. Therefore, the degree of constructive and destructive interference between the waves will vary cyclically and so therefore will the intensity detected at the detector. Thus the intensity at the detector is an indication of the relative lengths of the arms.
Several different methods of measuring distance using an interferometer are known. In the simplest, differential interferometry, the phase of a wave that has passed down a first arm, of known length, and the phase of a wave that has passed down a second arm, of unknown length, are compared in the manner described above. As explained above, the intensity detected at the detector will be between a maximum (full constructive interference, when the wave from each arm is in phase) and a minimum (full destructive interference, when the wave from each arm is in anti-phase). The change in path length required to move from the maximum to the minimum is half a wavelength (which would be, for example, a few tenths of a micron for visible light), and so this technique allows an unknown length change of the arm to be determined very precisely. However, because the intensity varies cyclically, the absolute length of the unknown arm is not determined: the intensity is the same for every whole wavelength of length difference, so only the remaining non-integer portion of the difference is determined.
In differential interferometry, the frequency of the wave must be fixed. In contrast, an alternative approach known as frequency-scanning interferometry (FSI) uses a source of waves having a frequency that can be varied (for an introduction to FSI, see Zheng J. “Optical frequency-modulated continuous-wave interferometers”, Applied Optics, 2006, 45, pp 2723-2730). In most FSI schemes, the waves are fed simultaneously into two interferometers: a reference interferometer having arms of known length and another, measurement, interferometer including a measurement arm, of unknown length that is to be determined. Providing the lengths of all arms remain constant, when the frequency of the waves is varied, the resulting change in the phase of the detected intensity in each interferometer is proportional to the optical path difference between the arms of that interferometer; equivalently, the ratio of optical path differences between the interferometers is equal to the ratio of the change in the phases in the detected signal. So if tuning over a fixed frequency interval results in the detected intensity in the reference interferometer passing through, say, 3 intensity maxima, and in the measurement interferometer, say, 6 intensity maxima, then the path difference between the arms of the measurement interferometer is twice as large as that between the arms of the reference interferometer. If the lengths of all interferometer arms except the measurement arm are known, the unknown length is determined.
FSI has the advantage that, in principle, the absolute order number of the interference fringes does not have to be determined, as measurement of the changes in the fringes with changing frequency is sufficient.
Regrettably, FSI tends to be less accurate and precise than the simple method of interferometry described above, particularly for long unknown distances. There are two main reasons for this. Firstly, most FSI systems measure length relative to the optical path difference of a ‘reference’ interferometer, whereas the simple method of interferometry described above measures length relative to a fixed laser wavelength. Limits in the accuracy of our knowledge of lengths of the reference interferometer optical path difference, or the fixed laser wavelength will degrade the accuracy of the final measurement. Typically it is easier to construct a laser with an accurately known fixed wavelength than it is to construct a useful reference interferometer with a length that is accurately known. Therefore FSI measurements are typically less accurate than measurements with the simple method of interferometry described earlier. Secondly, the nature of an FSI measurement is such that it is more sensitive to errors in determining the phase of the interferometers than differential interferometry is. i.e. a given error in phase measurement will lead to a larger error in distance measurement in FSI than in differential interferometry.
FSI also suffers from an error commonly known as ‘drift error’ whereby if the measured length changes during a measurement, this creates an error in the distance measurement that is typically much larger than the drift itself, being magnified by the ratio of the scan average frequency to the change in frequency over the scan.
Drift can often be limited at least to some extent by controlling the environment of the interferometers. Where that is not possible or not sufficient, various other methods of ameliorating the effects of drift exist. For example, Kinder T and Salewski K. “Progress in absolute distance interferometry based on a variable synthetic wavelength”. Messtechnik. (1) describe an FSI system utilising superheterodyne interferometry, in which the FSI phase measurements are made at beat frequencies generated between a first, fixed-frequency, laser and a second, tunable, laser. In this case, the change of beat frequency over the scan is twice the scan average frequency, and so the magnification of the drift is 0.5 (i.e. the error in the measurement of the unknown length is smaller than the relative interferometer drift). However, the Kinder system suffered from slow recording of multiple measurements, and an improved system was developed by Bechstein K and Fuchs W, “Absolute interferometric distance measurements applying a variable synthetic wavelength”, Journal of Optics. 1998; 29:179. This system utilised specialised optics, based on a Kösters prism, to generate four phase quadrature signals (one for each of two orthogonally polarised waves from two tunable lasers). Use of the quadrature signals enabled simultaneous measurement of the interferometer phase for each laser. The lasers were tuned in opposite directions, to reduce the effects of interferometer drift.
FSI has also been carried out without using a reference interferometer. Barwood G, Gill P and Rowley W describe in “High-accuracy length metrology using multiple-stage swept-frequency interferometry with laser diodes”, Measurement Science and Technology, 1998, 9(7), pp 1036-1041 an FSI-like technique in which, rather than using a reference interferometer, uses the beat frequencies between, on the one hand, a laser locked successively to two different spectral absorption features of rubidium and, on the other hand, a laser scanned in frequency between start and end points that are locked to etalon peaks. Barwood's method builds up accuracy by using sequentially larger frequency sweep ranges.
Another approach to FSI, using fast, coarse tuning and fine-tuned subscans, was implemented by Fox-Murphy A, Howell D, Nickerson R, and Weidberg A “Frequency scanned interferometry (FSI): the basis of a survey system for ATLAS using fast automated remote interferometry”, Nuclear Instruments and Methods in Physics, 1996; 383(1):229-237. Another, using linked subscans, has been implemented by Coe P A, Howell D F and Nickerson R B, “Frequency scanning interferometry in ATLAS: remote, multiple, simultaneous and precise distance measurements in a hostile environment” Measurement Science and Technology 2004; 15(11):2175-2187.
Coe Pa, Howell D F, Nickerson R B in “Frequency scanning interferometry in ATLAS: remote, multiple, simultaneous and precise distance measurements in a hostile environment”, Measurement Science and Technology, 2004; 15(11):2175-2187 describe a technique that simultaneously makes two FSI distance measurements of a distance, using a pair of tunable lasers. By varying the frequencies of each of these lasers in opposite directions, the error that occurs due to a change of distance during the measurement is also opposite for each of the two measurements. Therefore by averaging these two measurements the error is cancelled out.
Swinkels B, Bhattacharya N, Braat J in “Correcting movement errors in frequency-sweeping interferometry.”, Optics Letters. 2005; 30(17):2242-2244 describe a way in which the error from a changing distance during an FSI measurement may be reduced. It takes FSI measurements with the laser frequency alternately increasing and decreasing. By using a weighted average of several consecutive measurements the effect of distance change during measurement may be reduced. This method takes several sweeps for a single distance measurement and cannot compensate well for distance changes that occur on timescales shorter than the time taken for a frequency sweep.
Yang H, Deibel J, Nyberg S, Riles K in “High-precision absolute distance and vibration measurement with frequency scanned interferometry”, Applied Optics. 2005; 44(19):3937-44 describe a system that measures vibration as well as absolute distance using a tunable laser, FSI-like measurement.
But, prior-art FSI systems cannot cope well with a changing optical path difference (OPD). The explanation for that starts with this equation relating phase φ to interferometer OPD, D, and laser frequency, ν:
                    ϕ        =                  2          ⁢          π          ⁢                      Dv            c                                              (        1        )            where c is the speed of light. An FSI distance measurement is essentially a measurement of the partial derivative of phase, φ, with respect to frequency, ν:
                    D        =                              c                          2              ⁢              π                                ⁢                                    ∂              ϕ                                      ∂              v                                                          (        2        )            
However, in practice, FSI systems do not measure the partial derivative. The interferometer's phase, φ, is affected by changes in distance, D, as well as frequency, ν. Therefore we must consider the total derivative as the measurable quantity:
                                          ⅆ            ϕ                                ⅆ            v                          =                                            2              ⁢              π                        c                    ⁢                      (                          D              +                              v                ⁢                                                      ⅆ                    D                                                        ⅆ                    v                                                                        )                                              (        3        )            
We can measure dφ/dν and ν. The FSI measurement itself is supposed to determine D. However there is another, unknown, parameter in this equation: dD/dν. That means that prior-art FSI systems cannot simultaneously precisely determine both the absolute distance, D, and the rate of change of distance with respect to laser frequency, dD/dν.
It is however possible to obtain some knowledge of dD/dν. A common way of obtaining this is to minimise dD by holding the measured distance stationary during the measurement, whilst simultaneously maximising dν by using a laser that sweeps its frequency as fast as possible. One can then make the approximation that dD/dν=0. That approximation leads to uncertainty in the measurement of D, however, which is often the dominant contribution to the overall distance measurement uncertainty in prior-art FSI systems.
Thus a drawback of current FSI measurement methods is that, if the distance measured changes (perhaps due to vibration) whilst the measurement is being made, that creates measurement errors many times larger than the scale of the movement itself. A common method of minimising the problem is to use tunable lasers with a large tuning range and/or rapid tuning rate (which reduces the magnification of the errors).
It would be advantageous to provide a method and apparatus in which the above-mentioned problems are eliminated or ameliorated.